Tunable strain soliton networks confine electrons in van der Waals materials

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Sliding and twisting van der Waals layers with respect to each other gives rise to moir\'e structures with emergent electronic properties. Electrons in these moir\'e structures feel weak potentials that are typically in the tens of millielectronvolt range when the moir\'e structures are smooth at the atomic scale. Here we report a facile technique to achieve deep, deterministic trapping potentials via strain-based moir\'e engineering in van der Waals bilayers. We use elasto-scanning tunneling microscopy to show that uniaxial strain drives a commensurate-incommensurate lattice transition in a multilayer MoSe$_2$ system. In the incommensurate state, the top monolayer is partially detached from the bulk through the spontaneous formation of topological solitons where stress is relieved. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of the honeycomb network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Honeycomb soliton networks thus provide a unique path to engineer an array of identical deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials.